Multiparticle Wannier states and Thouless pumping of interacting bosons

The study of topological effects in physics is a hot area of research, and only recently have researchers been able to address the important issues of topological properties of interacting quantum systems. But it is still a great challenge to describe multiparticle and interaction effects. Here, we introduce the multiparticle Wannier states for interacting systems with cotranslational symmetry, which provide an orthogonal basis for constructing effective Hamiltonians for the isolated bands. We reveal how the shift of multiparticle Wannier state relates to the Chern number of the multiparticle Bloch band and study the Thouless pumping of two interacting bosons in a one-dimensional superlattice. In addition to the Thouless pumping of bound states when two bosons move unidirectionally as a whole, we describe topologically resonant tunneling when two bosons move unidirectionally, one by the other, provided the neighboring-well potential bias matches the interaction energy. Our work creates a paradigm for multiparticle topological effects and provides a way to detect topological states in interacting multiparticle systems.